Modeling Oscillating Systems: Physics Component Activities and Procedures

### 1) Engagement Activity - 90 minutes

Oscillation Explorations -

Each lab group is given an example of oscillatory motion to investigate.Through a guided discovery students will recognize and describe properties of oscillatory motion. Each group will prepare a brief presentation on specific aspects of the system they observe. Through class discussion similarities among the various examples will be highlighted.

Sample activities could include investigating:

1. A mass attached to a horizontal spring
2. A mass attached to a vertical spring
3. A hydrometer floating in a liquid
4. A simple pendulum
5. A frictionless U-tube of constant cross-sectional area containing liquid
6. A flat disc supported by a wire through its center that exhibits rotational oscillation
7. A horizontal string fixed at both ends, under constant tension, suspending a mass at the center
8. An inertial balance
9. A tuning fork
10. A metal rod fixed at one end
11. A marble rolling back and forth in a glass bowl

### 2) Concept Map Assessment - Homework

Following student presentations of similarities in their investigations of oscillatory motion, the teacher will lead a discussion that summarizes information and leads to definitions of terms, such as, period, frequency, and amplitude. Students will then be asked to make a preliminary concept map that demonstrates their understanding of oscillatory motion. The concept maps will be collected and compared with concept maps created at the end of the unit.

### 3) Horizontal Spring Investigation - 45 minutes

Students will explore the oscillatory motion of a low friction cart attached to a horizontal spring.They will collect data using CBL or MBL technology using motion and force probes. The purpose of this activity will be to collect real-time data that will be used to display the position, velocity, force, and acceleration of the cart over time. Students will also use the data to measure specific properties of the motion such as amplitude, period, and frequency.

### 4) Restoring Force Investigation - 45 minutes

Students will explore the nature of the restoring force in a spring. The purpose of this activity is to collect and analyze data from which they will develop the concept of a restoring force. The data will also enable calculation of the spring constant.

### 5) Stella Modeling and Exploration of Causal Connections - 90 minutes

Students will design and build a Stella model of a mass exhibiting oscillatory motion when attached to a horizontal spring. Students will use information from the previous two investigations (activity 3 and activity 4) to guide the design of the model and verify its accuracy.

The students will continue work with the horizontal spring model by exploring the relationship between period, spring constant, and mass using their model to acquire new data that can be analyzed with graphical analysis techniques. They will employ the technique of controlling and altering variables in order to determine causal connections.

Building the Horizontal Spring Model

### 6) Mathematics Collaboration - Included with Activities 5 and 6

Physics students will prepare summaries of their lab observations and data from the Stella model. These reports will be sent to math classes for mathematical analysis. The math students will mathematically analyze and model the data using Excel and/or Mathematica applications, and prepare a formal response describing their analysis for the physics students. The physics students in turn could use this response to confirm and build further connections between the mathematical model and measured quantities from previous experimental investigations.

### 7) Further Model Manipulation and Experimental Verification - 45 minutes

Students will first use the Stella model of the horizontal spring to explore quantitative effects associated with changing the amplitude of the oscillating mass. Students can then use experimental techniques to test and verify predictions associated with the model.

### 8) Model/Concept Extensions - 90 minutes

Student lab groups will be assigned an oscillatory system other than the mass attached to a horizontal spring. They will be given a description of the restoring force in each situation. They will then build a working Stella model of the system and determine which variables affect the frequency of oscillation. Groups will prepare a whiteboard (or similar) presentation of their system analysis. Students will be encouraged to convert Stella models to Java to create a presentation tool.

Possible systems to explore:

1. A mass attached to a vertical spring
2. A hydrometer floating in a liquid
3. A simple pendulum
4. A tuning fork
5. A metal bar fixed at one end
6. A marble in a glass bowl

Model Concept Extensions Worksheet

### 9) Concept Map Revisited - 30 minutes

Students will make a final concept map that demonstrates their understanding of oscillatory motion. They will compare this map with their preliminary concept maps and provide a written description of the changes in their thinking and understanding.